The invention is particularly applicable to a direct memory access controller for transferring data from several data sources to at least one addressee of these data, through several buffer memories each comprising a predetermined number of successive elementary memory locations, the access controller comprising a read management module designed to read data stored in the buffer memories and to transfer them in sequence to the addressee, and read pointer storage means associated respectively with each buffer memory, each read pointer indicating an elementary location of the buffer memory with which it is associated in which data can be read.